Mathematics
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Danny Pak-Keung Chan
  • Member for 5 years, 8 months
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All Questions Answers
Score Newest
answer
11
If $\int_a^bg(x)dx=0$, show that $\int_a^bf(x)g(x)dx=0.$
May 20, 2019
answer
11
Spivak's Calculus: chapter 2, problem 18(c)
Aug 5, 2020
answer
9
If $f$ is measurable and $fg$ is in $L^1$ for all $g \in L^q$, must $f \in L^p$?
May 12, 2019
answer
8
$f_n \rightharpoonup f$, $g_n \to g$ in measure, $\|g_n\|_{L^\infty} \leq M$, then $f_n g_n \rightharpoonup fg$,
Jun 30, 2018
answer
8
Proof: If $f : [a,b] \to [0,M]$ is Riemann integrable and has integral zero then $f(x) = 0$ at every continuity point $x$ of $f$.
Jul 22, 2017
answer
7
Prove that $\binom{n}{0} ^2 + \binom{n}{1} ^2 + \binom{n}{2} ^2 + ... + \binom{n}{n} ^2 = \binom{2n}{n}$.
Feb 23, 2020
answer
6
For a differentiable function $f$ show that $\{x:\limsup_{y\to x}|f'(y)|<\infty\} $ is open and dense in $\mathbb R$
Dec 14, 2019
answer
6
Convergence in measure - product
Jul 7, 2017
answer
6
Conditional expectation for a sum of iid random variables: $E(\xi\mid\xi+\eta)=E(\eta\mid\xi+\eta)=\frac{\xi+\eta}{2}$
Aug 7, 2017
answer
5
Do fog and gof uniquely determine f and g?
May 13, 2021

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